This feature is GNOME's Drive Mount applet. See 'man drivemount_applet' for more info. You probably removed it from the panel by mistake. It is available (though not active) by default in a standard GNOME installation.

For several months, I had a nice feature.
When I put in a USB memory, an icon would appear
in the panel at the top, with which I could unmount that device
and also check whether it was currently mounted or not.

But an upgrade a few weeks ago eliminated that feature.

Does anyone know what the feature was, and why it went away,
and how I can turn it back on?

It was a convenient feature and I recommend making sure it
is available by default.